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Bispidine-iron (II) complexes as a novel platform for the
design of magentogenic probes
Jacek Lukasz Kolanowski
To cite this version:
Jacek Lukasz Kolanowski. Bispidine-iron (II) complexes as a novel platform for the design of ma-gentogenic probes. Other. Ecole normale supérieure de lyon - ENS LYON, 2013. English. �NNT : 2013ENSL0849�. �tel-01059820�
N° national de thèse: 2013ENSL0849
THÈSE
en vue d’obtenir le grade deDocteur de l’Université de Lyon, délivré par l’École Normale Supérieure de Lyon
Discipline: Chimie
Laboratoire de Chimie, UMR 5182
École Doctorale de Chimie de Lyon, ED 206
présentée et soutenue publiquement le 30/10/2013
par M. Jacek Lukasz KOLANOWSKI
Bispidine-iron(II) complexes as a novel platform
for the design of magnetogenic probes
Directeur de thèse : M. Jens HASSERODT Après l'avis de : M. Frédéric BANSE
M. Kay SEVERIN Devant la commission d'examen formée de :
M. Frédéric BANSE, Professeur à Université Paris-Sud XI, Rapporteur M. Peter COMBA, Professeur à Universität Heidelberg, Examinateur
M. Jean-Pierre DUTASTA, Directeur de Recherches (CNRS) à l’ENS de Lyon, Président M. Jens HASSERODT, Professeur à l’ENS de Lyon, Directeur de thèse
I would like to dedicate this manuscript to my uncle Antoni who has passed away during the time of its preparation. He will always remain for me a distinct example of a noble, hard work as well as a selfless devotion to relatives and friends.
Chciałbym zadedykować ten manuskrypt mojemu wujowi, Antkowi, który odszedł do wieczności w czasie jego powstawania, a którego życie pozostanie dla mnie na zawsze niedoścignionym przykładem szlachetnej, ciężkiej pracy oraz bezinteresownego i całkowitego poświęcenia dla bliskich.
Acknowledgements
It is my great pleasure to thank Jens Hasserodt for giving me the opportunity to work on this project, which gave me a lot of satisfaction and enabled my scientific development. I am very grateful for the unusual trust, understanding, unique intellectual stimulation and many other things, that I have received in those nearly four years, both on the professional and personal level.
I would like to express my gratitude to Frédéric Banse and Kay Severin for accepting the role of the referees of my manuscript, for their valuable comments and flexibility. I would like also to sincerely thank Jean-Pierre Dutasta and Peter Comba for agreeing on joining the examination committee.
I am very grateful to the collaborators, with whom I had a great pleasure to work. I thank Marc Janier and David Kryza for their interest and fruitful cooperation on the “hot iron” project, to Erwann Jeanneau for the X-ray experiments, Dominique Luneau and Ruben Checa for the measurements of solid state magnetic moment, Olivier Beuf and Laurence Canaple for the MRI experiments and Pauline Bonazza for the biodistribution studies.
My warmest thanks go to the co-workers from the Organic Biochemistry Group, to Jinping, Guillaume and Oliver for the unique atmosphere in our “Bureau International” as well as to the “anciens”: Monica, Anna and Yevgen. Thanks to you coming to work every day (and sometimes during the night) for the last 4 years was for me like coming home. I would like also to thank Fayçal for the inspiring discussions, Maxime for an open-mindedness and translations, Benjamin, Charlene, Corentin, Delphine, Emma, Pauline, Philippe, Sean, Sylvain and those who, despite their short stay, have left unforgettable memories: Cai and Paula as well as Robert and Hanno, who I had a great pleasure to supervise during their internships. Thank you all for providing such an enjoyable work place and turning these years of my French adventure in a truly happy time.
I am very grateful to all colleagues from the whole chemistry department, which made the ordinary working days very pleasant (and efficient!), to Philippe for the care over LC/MS and friendly conversations, Christophe for the “electrochemical” training and good words, Jean-Christophe and Delphine for their smile and good humor, Sandrine for help with the NMR, Menaf, Martin, Julien, Yann, Sébastien, Quentin, Adrien, Thorsten, Yuting, Martine, Alexandre, Laure-Lise, Bastien(s) (les deux ), Olivier… Great thanks also to “the biologists”, especially to Gosia, Julia, Monika, Armel, Morgan, Lama and Imtiaz, being always so warm and helpful.
I do not know how to thank those with whom I have spent wonderful moments outside of the laboratory. I am really grateful to Monica, Fabrice and petit Maxence, les Espagnoles (los Polacos ) “Anna-Catalana” and Julien, as well as the great group of “foreigners” who shared with me all the good and bad moments of the life of the PhD student - Adi, Cristi, Emel, Michel, Robert, Kaja, Menaf, Guillaume... I will also never forget my team-mates with whom I shared my great passion to football, in particular Remy, Eric, Jocelyn, Sergey, Anghel, Djamel, “Padre” Benjamin and dozens of other colleagues that I met every week to “taper le ballon”.
I would like to thank the „Polish team” from the Paroisse Sainte Trinité, which enriched the last year of my stay in Lyon. I thank Agnieszka, Inga, Kasia, Magda, Grzegorz, Mateusz Z., Mateusz P., Piotr and Agnieszka, Father Tadeusz Śmiech and especially Father Paweł Witkowski, whose attitude and faith have helped me in finalizing my work.
I am also very grateful to those who could not be here in Lyon physically, but remained friends independently on circumstances - to Miłosz, Marta, Łukasz and Michał, Dominika and Łukasz. There are countless things and no suitable words in which I can thank Gosia, who not only largely contributed to my arrival to France, but who also found, luckily for me, enough strength to stay next to me during those ”French years”.
I cannot find a simple way to properly express my deep gratitude to my family for their invaluable mental and physical support, which I felt constantly, independently on the circumstances, even from the distance of 1500 km. To my parents, Łucja and Edward for 28 years of their unconditional love and beautiful example; to my sister Ania for her visits and endless speeches on the phone, my brother Tomek for his true fraternal friendship and Agnieszka for having for me always some good words and tolerating my “apartment squatting” at least few times a year.
Nie mogę znaleźć prostego sposobu, żeby właściwie wyrazić wdzięczność mojej rodzinie za jej bezcenne wsparcie psychiczne i fizyczne, które niezależnie od okoliczności czułem nieustannie nawet z odległości 1500 km. Moim rodzicom, Łucji i Edwardowi, za 28 lat ich bezwarunkowej miłości i pięknego przykładu, mojej siostrze Ani za jej wizyty i niekończące się opowieści przez telefon, mojemu bratu Tomkowi za prawdziwą, braterską przyjaźń i Agnieszce za dobre słowo oraz tolerowanie w swoim domu takiego „intruza” jak ja przynajmniej kilka razy do roku.
Last but not least I would like to thank my school and academic teachers who have developed in me the curiosity towards the surrounding world and “shaped” me as an adult and as a young scientist at the beginning of his adventure. I thank my former teachers: Danuta Jastrzębska and Małgorzata Adamiak, as well as Małgorzata Konarczak-Tymek, Hanna Heimlich and Karol Kacprzak who initially instill in me passion to chemistry. I would like to express my warm gratitude to Henryk Koroniak for his encouragement, kindness and “scientific travel agency” which enabled me to broaden my horizons, as well as Gerd-Voelker Roeschenthaler, Sergey Tverdomed, Romana Pajkert and Przemysław Wojtaszek, all of whom played very important role in my “bio-chemical” upbringing
Détails pratiques
Ces travaux de thèse (01/01/2010 – 31/12/2012) se sont déroulés sous la direction du professeur Jens Hasserodt, dans l’équipe de Chimie Bio-Organique, au Laboratoire de Chimie de l’École Normale Supérieure de Lyon, 46 Allée d’Italie, 69007 Lyon, France. Les travaux avec du matériel radioactif ont été realisé au laboratorie de la Fédération de Médecine Nucléaire – Radiopharmacie dirigé par le professeur Marc Janier, à l’Hôpital Edouard Herriot (Lyon), 5 place d’Arsonval, 69437 Lyon cedex 03, France. Tous les travaux expérimentaux décris dans ce manuscrit relèvent de mon travail personnel sauf mention explicite du contraire.
TABLE OF CONTENT
Abstract ... 10
Résumé ... 11
Abbreviations ... 12
STATE OF THE ART ... 17
1. MAGNETIC READOUT AS A DETECTION MODE ... 19
1.1. Detecting a chemical stimulus in solution by responsive probes... 19
1.2. Molecular and electronic origins of magnetism ... 20
1.3. Magnetic Resonance Imaging in the detection of paramagnetism ... 26
2. MAGNETIC RESPONSIVENESS IN METAL COMPLEXES ... 39
2.1. Introduction to LS-HS equilibria in transition metal complexes ... 40
2.2. Magnetic responsiveness in solution upon chemical stimulus... 47
3. TOWARDS MAGNETOGENIC MOLECULAR PROBES IN METAL COMPLEXES ... 58
3.1. Hallmarks of probe’s design – a power of magnetogenesis ... 58
3.2. (Para)magnetogenesis – magnetic off-ON activation ... 60
3.3. First magnetogenic design for detection of chemical reactivity ... 61
3.4. Bispidines – promising molecular platform for iron(II) ... 66
RESULTS AND DISCUSSION ... 71
4. OBJECTIVES OF THE PROJECT ... 73
5. NOVEL SYNTHETIC INTERMEDIATE FOR PREPARATION OF BISPIDINE LIGANDS ... 75
5.1. Rationale behind the choice of optimal N5 platform ... 75
5.2. Classic synthetic methodology ... 77
5.3. Alternative synthesis of N7-H platform – protecting group ... 81
5.4. Deprotection – removal of DMB ... 88
5.5. Perspective - PMB as alternative protecting group ... 92
5.6. Conclusions ... 92
6. BISPIDINE-BASED MAGNETIC OFF-ON DUO ... 93
6.1. Introduction – the concept of overcoming a steric clash ... 93
6.2. Synthesis of hexadentate bispidine ligands... 95
6.3. Complexation and solid state structures ... 98
6.5. Summary ...116
7. MAGNETIC EQUILIBRIA IN BISPIDINE-IRON(II) SYSTEM ... 117
7.1. Temperature and solvent dependency of magnetic equilibria –ternary vs. binary complex117 7.2. Anion sensitivity – towards magnetogenic anion sensors ...130
8. BISPIDINE-IRON(II) SYSTEM IN MRI ... 144
8.1. Relaxivities of a pair of off-on model chelates and their MRI characterization ...145
8.2. Off-ON activation in MRI...152
8.3. Perspectives – towards the response at physiological conditions...159
8.4. Fine tuning of the physico-chemical properties of bispidines by periphery modification ...165
8.5. Summary ...172
9. RADIOLABELING OF IRON(II) COMPLEXES TO STUDY BIODISTRIBUTION IN VIVO ... 173
9.1. Intro – motivation, objectives and state of the art ...174
9.2. Development of the radiolabeling protocol ...175
9.3. Validation of the protocol - model in vivo study ...181
9.4. Conclusions ...185
CONCLUSIONS AND PERSPECTIVES ... 187
10. SUMMARY OF ACHIEVEMENTS ... 189
11. GENERAL PERSPECTIVES ... 191
11.1. MRI detection of in vivo enzyme activity by 3-component bispidine-iron(II) probes ...191
11.2. Switchable catalysis upon coordination sphere opening ...192
11.3. Magnetogenic probing without opening of coordination sphere ...192
EXPERIMENTAL ... 195
SYNTHESIS ... 197 General Procedures ...197 Organic synthesis ...199 Complexation ...224 X-RAY STRUCTURES ... 236 General procedures ...236 Ligands’ structures ...237 Iron(II) complexes ...239NMR AND MAGNETIC MOMENTS AT VARIED TEMPERATURE ... 246
General procedures ...246
Temperature-dependency of magnetic moments of SCO complex ... 252
Variable-temperature magnetic behavior of other complexes ... 256
TITRATION EXPERIMENTS –ANIONS’ INFLUENCE ON [FE15] (IN MEOH) ... 261
UV-Vis Data ... 261
Magnetic Moment uponthe addition of anions ... 262
Estimations of binding constants ... 263
IN VIVO STUDIES ... 264
MR in vivo images of mice ... 264
Biodistribution studies with radioactive compound ... 266
BIBLIOGRAPHY ... 267
APPENDICES ... 277
PUBLICATIONS FROM THIS PHD ... 279
10
Abstract
Bispidine-iron(II) complexes as a novel platform for the design of magnetogenic probes
This work concerns the development and characterization of molecular probes that respond to a chemical analyte in a liquid sample by turning from a diamagnetic to a paramagnetic state (off-on mode).
With the aim of designing these tools, we focused on iron(II) chelates of bicyclic bispidines as they promised, among others, sufficient probe stability, even in competitive media like water. This manuscript describes new robust synthetic protocols for their large-scale preparation. Synthesized bispidine-iron(II) complexes were thoroughly characterized in solution (1D/2D NMR, MS, UV-Vis, CV) and in the solid state (X-ray and SQUID). In particular, I report here the first diamagnetic, low spin examples thereof, as well as pairs of structurally related diamagnetic-paramagnetic chelates. It now enables the design of responsive probes for various (bio)-chemical targets (including enzyme biomarkers), accessible by one-step functionalization of a key synthetic intermediate with suitable trigger moieties. The first two such probes are described herein, which respond to the presence of a particular kind of anion or a change in the pH.
In addition, in the course of my work, the unprecedented radioactive iron(II) (Fe-59 isotope) complex of a model water-insoluble ligand was prepared and used in an initial biodistribution study in mice. This original protocol can now be directly adapted to virtually all iron(II)-based probe candidates. Furthermore, the relaxivity data obtained for model MRI-silent and MRI-active chelates, in conjunction with the in vivo behavior of the active form in mice, bode well for a creation of an MRI probe functioning in a true off-on mode.
Methodologies and molecular designs described herein enable the development of solution-operating magnetogenic molecular probes, which until now have not been synthesized. The availability of such tools would open up numerous perspectives for technological, environmental and biomedical applications.
Keywords: responsive molecular probes · bispidines · iron(II) · MRI · spin transition ·
magnetism · imaging agents · water
11
Résumé
Les complexes de bispidines-fer(II): une nouvelle plateforme
pour le design de sondes magnétogéniques.
Cette thèse décrit le développement et de la caractérisation de sondes moléculaires répondant à des analytes chimiques en solution par le passage d’un état diamagnétique à un état paramagnétique (mode off-on).
Dans le but de concevoir de tels outils, nous avons focalisé notre attention sur les chélates de fer(II) avec des ligands de type bispidine bicyclique puisqu’ils présentent, entre autres, une stabilité suffisante même en milieux compétitifs comme l’eau. Ce manuscrit décrit des protocoles synthétiques robustes pour leurs préparations à grande échelle. Les complexes synthétisés ont été entièrement caractérisé en solution (RMN 1D/2D, MS, UV-Vis, CV) et dans l’état solide (rayon X et SQUID). Je suis notamment parvenu à synthétiser le premier exemple de complexe bispidine-fer(II) diamagnétique, bas spin, ainsi qu’à proposer des paires de chélates diamagnétique-paramagnétique aux structures connexes. Nous avons donc à notre disposition un système magnétique off-on valide, qui permet le design de sondes répondant à un stimulus (bio)-chimiques (biomarqueurs enzymatiques par ex.) par fonctionnalisation d’un synthon clé en une seule étape. Les deux premières sondes de ce type sont décrites ici, une répondant à la présence d’anions particuliers et l’autre répondant au pH.
Au cours de ce travail, nous avons également mis au point la préparation du tout premier complexe de fer(II) radioactif avec un ligand insoluble en milieu aqueux et nous l’avons utilisé pour faire une étude préliminaire de biodistribution chez la souris. Ce protocole original pourrait être adapté pour virtuellement toute sonde à base de complexes de fer(II). Les données de relaxivité obtenues pour les modes silencieux et actif en IRM en conjonction avec le comportement in vivo de la forme active chez la souris semblent être prometteuses quant à la création d’une sonde IRM fonctionnant sur le principe du mode off-on.
Les méthodologies et designs moléculaires présentés ici ouvrent le champ au développement de sondes moléculaires magnétogéniques opérationnelles en solution, qui n’avait, pour l’heure, jamais été synthétisé. L’avènement de tels outils présente de nombreuses perspectives pour des applications dans les domaines technologiques, environnementales et biomédicales.
Mots-Clés : sondes moléculaires répondeurs · bispidines · fer(II) · IRM· transition de spin
· magnetisme · agents d’imagerie · eau
12
Abbreviations
Textual abbreviations
bistet-tacn 1,4-bis(5-tetrazolyl)methyl-1,4,7-triazacyclononane
bispidine 3,7-diazabicyclononane nd its derivatives
BOLD-fMRI blood-oxygen-level dependent functional magnetic resonance imaging
Bpy Bipyridine
Bzimpy bis-benzimidazolepyridine
CA (or CAs) contrast agent (or contrast agents)
CN coordination number
COSY correlation spectroscopy (2D NMR)
CPP cell penetrating peptide
CS Curie spin relaxation mechanism
CV cyclic voltammetry
DCM Dichloromethane
DD dipole-dipole interaction (relaxation mechanism)
DDQ 2,3-dichloro-5,6-dicyano-1,4-benzoquinone
Dept distrotionless enhancement by polarization transfer (C-13 NMR experiment)
DIMS (MS) direct injection mass spectrometry (also abbreviated MS)
DIPEA (N,N-diisopropyl-N-ethylamine – Hunig base
DMB 2,4-dimethoxybenzyl moiety
DMF Dimethylformamide
DMSO Dimethylsulfoxide
DOTA 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid and all its conjugated bases
dptacn / tptacn 1,4-dipicolyl-1,4,7-triazacyclononane / 1,4,7-tripicolyl-1,4,7-triazacyclononane.
DTPA diethylene triamine pentaacetic acid (Pentetic acid) and all its conjugated bases
En Ethylenediamine
[FeX(Y)]Z complex of iron with polydentate ligand X, monodentate ligand Y both being directly coordinated to the metal centre and Z is the counterion
GBCAs gadolinum-based contrast agents
HMBC Heteronuclear multiple-bond correlation spectroscopy (2D NMR)
HOMO / LUMO lowest unoccupied molecular orbital
HRMS high resolution mass spectroscopy
HS high spin
HSA human serum albumin
HSQC Heteronuclear single-quantum correlation spectroscopy (2D NMR)
IDA indicator displacement assay
iPrOH iso-propanol (propan-2-ol)
IR Infrared spectroscopy
13
Jmod j modulation (C-13 NMR experiment)
LS low spin
MLCT metal-to-ligand charge transfer band
MR, MRS Magnetic Resonance, Magnetic Resonance Spectroscopy (imaging modality)
MRI (fr. IRM) Magnetic Resonance Imaging (Imagerie par Résonance Magnétique)
NMR (1D and 2D) Nuclear Magnetic Resonance (one- and two-dimensional techniques)
NOESY Nuclear Overhauser effect spectroscopy (2D NMR)
Oxdz 1,2,4-oxadiazole or oxadiazolyl moiety
Ozd Oxazolidinone or oxazolidinolyl moiety
paraCEST paramagnetic Chemical Exchange Saturation Transfer
PB / PBS phosphate buffer / phosphate buffer saline (1x concentrated)
Pdz 2,3-pyridazine and pyridazinyl moiety
PET Positron Emission Tomography
phen Phenantroline or phenantrolinyl moiety
pi = picolyl (2-pyridyl)metyl moiety
PMB paramethoxybenzyl moiety
PRE paramagnetic relaxation enhancement
Py 2-pyridine or 2-pirydyl moiety
RF radiofrequency impulse
RT room temperature
SBM Solomon-Bloembergen-Morgan theory
SC scalar coupling (relaxation mechanism)
SCO spin crossover
SNR signal-to-noise ratio
SPECT Single Photon Emission Computed Tomography
SPIO Superparamagnetic iron oxide nanoparticles
SQUID superconducting quantum interference device
Tacn 1,4,7-triazacyclononane
Tf trifluoromethanesulfonate (triflate)
TFA trifluoroacetic acid / trifluoroacetate
THF tetrahydrofuran
TLC thin layer chromatography
Tren tris(2-aminoethyl)amine
Tris 2-hydroxymethyl-2-amino-1,3-propanediol
Ts para-toluenesulfonyl; thus TsOH: para-toluenesulfonic acid
USPIO ultrasmall superparamagnetic iron oxide nanoparticles (ultrasmall SPIO)
UV-Vis ultraviolet-visible light spectroscopy
ZFS zero-field splitting
14
Analytical variables and parameters
A, B, C Racah parameters
A/ℏ hyperfine (or scalar) coupling constant (in here: between the proton of water in the first coordination sphere and the electron spin of the paramagnetic center); (theory of relaxation)
B0 [T] external magnetic field (in the NMR experiment)
B1 vector of the magnetic field generated by the radiofrequency excitation impulse in the NMR experiment
β nephelauxetic effect parameter - ratio between Racah B parameter in the complex (B’) to the one of free ion in gaseous state (B) γ, γI
[rad s−1 T −1] gyromagnetic ratio, γI = nuclear gyromagnetic ratio
DN [kcal mol-1] Gutmann's donor number - energy released upon the formation of the 1:1 complex
between Lewis base and the standard Lewis acid SbCl5 δd, δp, δH
[MPa1/2] Hansen solubility parameters: energy from dispersion forces (δforce (δ d), dipolar intramolecular
p) and hydrogen bonds (δH) between the molecules
Δ0 [cm-1] d-orbitals’ splitting energy (10 Dq)
δ [ppm] chemical shft of the nucleus (in parts per milion) measured from the nuclear reference
Δδ [ppm] isotropic shift = change in the chemical shift upon the appearance of a paramagnetic quality in an originally diamagnetic sample ∆Ho [kJ mol-1] molar standard enthalpy of spin-transition process
∆So [J mol-1] molar standard entropy of spin-transition process
ε [M-1cm-1] molar extinction coefficient = molar absorptivity (in UV-Vis spectroscopy)
f , h dimentioneless d-orbitals splitting (f) and d-electrons pairing (k) energy parameters of a ligand in octahedral complexes (Jorgensen equations)
g electron g-factor (paramagnetic relaxation enhancement equations)
g [cm-1] d-orbitals splitting energy parameter of a metal ion in octahedral complexes (Jorgensen
equation)
J [Hz] The internuclear coupling constant (NMR experiments)
k dimentioneless d-electrons pairing energy parameter of a metal ion in octahedral complexes (Jorgensen equation) K1 thermodynamic constant of the reaction (of the spin transition LS<->HS)
K2 thermodynamic binding constant of an anion to the HS form of the complex
L total orbital angular momentum of the unpaired electrons
M0 net magnetization vector (for a sample in the external magnetic field) µ: µeff, µHS, µLS,
µHSA , µe, µp,
[µB]
magnetic moment: µeff = effective (observable) magnetic moment, magnetic moment of
the high spin (µHS), low spin (µLS) and high spin-anion bound (µHSA) forms respectively,
µe = magnetic moment of electron, µp = magnetic moment of the proton, µB = Bohr
magneton = 9.27*10-24 [J T-1]
µ0 [T m A-1] vacuum permeability = magnetic constant ≈ 1.2566*10-6
P [cm-1] effective d-electrons’ pairing energy
15
pKa negative decimal logarithm from the thermodynamic constant of acid dissociation reaction: K
a = [A][H]/[AH] of the reaction HA A- + H+
Pm molar fraction of bound water (in paramagnetic relaxation enhancement theory)
π “pi” molecular orbital, usually in the context of π-boniding (π-donation or π-accepting) - interaction involving the pi orbitals
q hydration number (number of coordination sites in the first coordination sphere occupied by water molecules) r(M-H) [m]
distance between the "relaxing" nucleus (proton) and unpaired electrons - in practice often approximated to the internuclear distance between H from water and paramagnetic metal ion
r: r1, r1IS, r1OS,
r1SS, r2
[mM-1s-1]
relaxivity (relaxation rate per unit concentration of the contrast agent): subscript 1 denotes relaxation rate of longitudinal compounent of magnetization vector and r2 refers to the
transversal one, superscripts IS, OS and SS refer to the contributions from the relaxation of water protons from the inner sphere (first coordination sphere) outer sphere (bulk) and second sphere (water bound to the periphery of the complex)
Rf retention factor in the TLC analysis (ratio of a distance covered by the product to the distance covered by the solvent)
S total spin angular momentum of the unpaired electrons
ΔI diffrence between total spin angular momentum of the two compounds (typically of high spin and low spin forms: S
HS - SLS where SHS > SLS and S is a spin angular momentum)
σ “sigma” molecular orbital, usually in the context of σ -bonding - interaction involving σ-orbitals
T [K] temperature
T1/2 [K] temperature of spin-transition (temperature in which the ratio of low spin high spin isomer is 1)
T1 : T1DD, T1SC,
T1,obs, T1,d,
T1,paramag
[s]
longitudinal (spin-lattice) relaxation time (T1) and contributions from dipole-dipole (T1DD)
or scalar coupling (T1SC) relaxation mechanism (theory of relaxation), T1,obs = effective
longitudinal relaxation time, in opurely diamagnetic environment (T1,d) and contribution
from the presence of the paramagnetic quality in the sample (T1,paramagn) T1e, T2e [s] longitudinal and trasversal electronic relaxation times
T1m [s] longitudinal relaxation time of the bound water protons
T2, T2* [s] transversal (spin-spin) relaxation times, Tinhomogeneities 2* = transversal relaxation time including field τ: τc, τe, τR, τm
[s] correlation times: ττR = rotational correlation time, τc and τe = specific correlation times of the relaxation process, m = water residence time; (theory of relaxation).
1/T, 1/τ [s-1] relaxation rates
ϕ, Δϕ [o] ϕ = torsional angle measured for the nearest Fe-N bond and respective C-H bond, Δϕ =
deviation of ϕ from the value of 90 o at which contact shift is quenched χ [emu K cm-1] magnetic susceptibility
Ω [MPa1/2] cavity term in Linear Solvation Energy Relationship for predicting solubility which corresponds to the Hildebrand solubility parameter (square root of cohesive energy
density)
ν [cm-1] The wavenumber of an excitation in IR spectroscopy in reciprocal centimeters
ν0 [s-1] Larmor frequency (resonance frequency of the non-zero spin nucleus in NMR experiment)
ω: ωS, ωI
[rad s-1] The angular Larmor frequency of electron (ωS) and proton (ωI) (theory of relaxation)
PART I
MAGNETIC READOUT AS A DETECTION MODE
19
1.
M
AGNETIC READOUT AS A DETECTION MODE
1.1.
Detecting a chemical stimulus in solution by responsive
probes
Small molecules which can generate a distinct physical signal as a consequence of the presence or reactivity of a chemical analyte in liquid samples are powerful tools for studying and monitoring a variety of technological, environmental and biochemical processes. They constitute an important part of a rapidly developing field of Chemical Imaging (are perfectly suited for this purpose)[1]. The whole range of physical readouts can a priori be envisaged as detectable signals, including electromagnetic waves (absorbance, fluorescence, phosphorescence, interferometry), highly ionizing radiation (radioactivity), acoustics, electric current (conductometry) and magnetism. They are adapted to sensing and imaging purposes to differing degrees and while some are already used in well established techniques, others still await wider recognition.
Responsive probes show distinct advantages over non-reactive ones that always emit a signal: in homogeneous liquid samples, only the use of the former is meaningful; but even in spatially structured, heterogeneous liquid samples (such as biological tissue) those unresponsive probes that have not found their target by simple binding, have to be evacuated to allow for the extraction of information by imaging. The effective removal of this excess proportion is often highly problematic leading to false positive detection, low signal-to-background ratios, and significantly diminish the reliability of the results. Some physical readouts are better suited for the design of agents responding to chemical targets than others. Radioactivity for example is virtually independent of the chemical environment/activity as it is determined by the nature of the nucleus. On the other hand optical properties stem from the electronic system of the molecule and thus are relatively easily modified by chemical interactions. Consequently, the majority of existing responsive probes for chemical stimuli are based on optical detection. (Para)magnetism is yet another property which might be tuned by altering the electronic organization/interactions and thus being available for the design of such tools, but magnetically responsive single-molecule probes for applications in solution are non-existent.
This work describes an original molecular design to address this challenge and hopes to inspire further efforts.
MAGNETIC READOUT AS A DETECTION MODE
20
1.2.
Molecular and electronic origins of magnetism
[2][3]1.2.1.
Introduction
Magnetism is a physical property of Matter, which results from its interaction with a magnetic field generated by another magnet. All moving charges a priori generate a local magnetic field which is characterized by the magnetic moment (angular momentum). In addition, an elemental particle has its intrinsic “spin”, so the angular momentum resulting from its precession is characteristic for each type of particle. The magnetic moment of an atom can be divided into three distinct magnetic contributions, differing in strength and derived from different elemental particles of which the atom is composed: a) electronic spin b) orbital angular momentum and c) nuclear spin.
A specific net value of the nuclear spin, characteristic for each isotope, results from the composition of the nucleus and interactions therein. It originates from the intrinsic spins of the nucleons (protons and neutrons), which are ca. three orders of magnitude smaller than the spin of electrons (the spin of a neutron is 960 times and that of a proton 658 times smaller). Consequently, its contribution to the overall magnetic moment is negligible (but it can be of great use when reporting on the electronic structure of the atom and molecules as seen in the case of Nuclear Magnetic Resonance (NMR) – see chapter 1.3.3), and the observed net magnetic moment is principally caused by electronic contributions
1.2.2.
Diamagnetic quality
In the atoms (and molecules) the majority of electrons are paired up (Pauli’s exclusion principle), meaning that they attain the spin of the opposite sign when occupying the same orbital, and thus their contribution to the overall magnetic moment is cancelled out. However, the electrons from the same orbital but of opposite spin respond differently to the magnetic field; dependent on the direction of the spin angular momentum (the sign of the spin) they will occupy the space slightly closer or slightly further from the nucleus. This will increase the contribution of the electrons with the spin in the direction opposite to the external magnetic field, and decrease the one parallel to it. In the result it gives rise to the net magnetic moment opposing the magnetic field and thus being repelled by it. The effect, called the diamagnetic contribution, is roughly proportional to the mass of the atom (number of electrons).
1.2.3.
Paramagnetism – the consequence of unpaired electrons
When electrons are unpaired, what means that the total electronic spin (sum of the electronic spins) is positive, the paramagnetic behavior is predominant and cancels out the diamagnetic effect. In this case the effective magnetic moment (µeff) can be given by a formula:
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(1)
where S is an overall sum of the electronic spin (spin angular momentum of the electrons), L is the total orbital angular momentum of the electrons (sum of the l quantum numbers of the unpaired electrons) and µB is Bohr-magneton.
This formula demonstrates that the electronic spin contribution is directly connected to the number of unpaired electrons which determines the value of (S) and in majority of cases it is dominant. Unlike the movement of the electrons within the particular orbital being at the origin of the diamagnetism, the orbital paramagnetic contribution results from the movement of the electron (electronic density) between the electronic orbitals around the nucleus. In order for it to occur, it needs the available vacancies (on the orbitals) of the same energy and symmetry. The initial degeneracy of multiple orbitals may be lost upon the formation of the compounds (approach of the ligand – see discussion below), thus quenching the orbital contribution.
Fig 1 removed
Fig. 1 Shape and annotation of electronic d-orbitals (taken from the web page [4]).
Secondly, the symmetry requirement is met only if the orbitals, between which the movement occurs, are related to each other by simple rotation along one of the axes; i.e. if considering the energetically degenerate d-orbitals (model situation of the isolated ions or in theoretical isotropic spherical ligand field – Fig. 1), the electron can “jump” between the dxy, dxz, dyz and orbitals thus contributing to overall paramagnetism. Only is excluded as its symmetry is different (Fig. 1) and thus it cannot take part in generation of the orbital angular momentum. In addition, the orbital to which the electron can be moved, should not yet possess the electrons of the same spin as the moving one, because this would require an extra energy in order to change the orientation of the spin (Pauli’s exclusion principle, see also the discussion on pairing energy below). Thus, the arrangement of the electrons and the energetic positioning of the d-orbitals will have a decisive influence on whether the magnetic moment will be purely a consequence of spin-only contribution or will also have the electronic movement-derived one. As the distance from the nucleus increases, the effects of the movement of the electrons will also be more pronounced, which is often explained by the increased electronic velocity and more pronounced “feeling” of the magnetic field by this charge [2]. In the consequence, the orbital contribution will depend to some extent on the Z atomic number. For lighter atoms (lower Z) it will be rather small, but in elements of higher Z, this contribution becomes increasingly important and may even be decisive in determining the magnetic moment. In fact, the existence of the orbital magnetic moment is always associated with the interaction between this and the spin angular momentum, which results in so called spin-orbit
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coupling. For heavier elements this effect is strong and thus the determination of the overall magnetic moment requires more complicated calculations (for example j-j coupling model). However, when the interaction is small, as for the lighter elements (like first row transition metals), then the spin and orbital contributions may be treated independently as in the equation above (Russell-Saunders coupling).
1.2.4.
Paramagnetism in isolated molecules
If the interaction between the paramagnetic centers occurs (like in the solid state), magnetic moments may spontaneously rearrange causing the appearance of permanent magnetic properties (e.g. ferro- or antiferro-magnetism), which persist also in the absence of the external magnetic field (permanent magnets). Recently, intensive research is pursued in the preparation of the single molecule magnets, where the permanent magnetism can also be stabilized in the isolated molecule. This is possible only when this molecule possesses at least two distinct paramagnetic centers that are still able to interact with each other.
This type of magnetic interaction is not possible in case of mononuclear molecules (one magnetic center per molecule) in solution, where they remain isolated due to the dilution effects (and the surrounding ligands), hence only two basic cases: diamagnetism or paramagnetism, are considered. The former is significantly less pronounced and, even if being an intrinsic property of all materials, it can only be observed in the absence of any paramagnetic contribution. Such materials are by convention often called “non-magnetic”. In the result, the paramagnetic behavior may be selectively detected over the diamagnetic background, what makes it a suitable physical readout for the reporting purposes. Hence, it is in fact the paramagnetic quality which stands behind the term “magnetic signal” and which is the focus of this work.
1.2.5.
Features of the paramagnetic signal
In comparison to other physical signals, magnetization offers convincing and attractive benefits: (1) High selectivity of the external magnetic field for the non-cancelled spins, which confer the
magnetic moment to the sample, promises a high specificity of the readout for many environments where no other paramagnetic quality exists.
(2) The magnetic signal offers almost no penetration limits as the external magnetic field penetrates most obstacles, and thus theoretically no need for local excitation is a priori required (unless resonance detection techniques are used – see below)
(3) The unique relative “inertness” of the magnetic field towards non-(para)magnetic species, as well as the “transitional” character of the magnetization, which is removed after the removal of the external magnetic field, makes this mode of readout environmentally harmless. This is not the case for many other physical signals, which often damage and permanently alter the molecule or the sample. For example, the highly ionizing radiation (gamma-radiation, electrons, etc) is known to be detrimental to the live organisms, similarly to UV which can
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alter chemical bonds. In addition, the visible light, or even IR, is diffracted and absorbed by the majority of matrices, leading not only to the distortion or even the loss of the signal but also delivers the energy to the system, heating it up and thus facilitating also a wide range of uncontrollable side effects, including chemical transformations.
(4) Magnetic signal does not experience any fatigue, commonly occurring for fluorescent or radio-active molecules.
(5) The newly arisen paramagnetic quality is often accompanied by the change of the other properties (like optical or conductive – electrical) and thus lead to the opportunity of an orthogonal readout providing the alternative advantages and hence significantly increasing also the applicability of such multimodal tools.
1.2.6.
Detection of paramagnetism
Paramagnetic quality can be detected by a variety of different methods and tools (force methods with Gouy’s and derived balances [5]; induction method-based SQUID device (superconducting quantum interference device) [6], Hall-sensors [7] and others [8]). In particular for solution studies, strategies based on the spin resonance are commonly used and dynamically developing. It is important to point out that they require the excitation of the sample, but the radiofrequencies used for this purpose share the high penetration capacity and environmental harmlessness, and thus do not impair the attractiveness of the magnetic readout as the detection tool (see subchapter 1.3.1, points (2) and (3)).
The direct detection of unpaired electrons within the sample is realized by Electron Paramagnetic Resonance (EPR, or ESR - Electron Spin Resonance). The “chemical shift” (resonance frequency) as well as the shape and splitting pattern of the signal may give a lot of information about the surrounding of the unpaired electrons, like other interacting spins (also nuclear spins) and parameters of the media. This method has already been applied in biological models where the so called spin labels (stable organic radicals) are used to tag the biological systems and on the basis of the changes in the signal obtained, the information about the polarity of the media as well as y and z can be drawn. This technique was proven to be useful in monitoring the protein interactions etc.
Indirect detection of paramagnetism by NMR is possible as unpaired electrons can influence both the chemical shifts (Evans’ method – see experimental part, Magnetic Resonance Spectroscopy (MRS), paraCEST effect (paramagnetic chemical exchange saturation transfer)) and the relaxation times of the selected nuclei (Magnetic Resonance Imaging (MRI) – see chapter 1.4). The main disadvantage of the NMR is its low sensitivity. The development of the more powerful detectors (bigger magnets – stronger magnetic fields) as well as application of the variable strategies of signal enhancement (for example hyperpolarization) try to address this problem.[1] On the other hand, large sizes of NMR device and very high costs are often a big problems, but recent
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progress in the construction of miniaturized, portable and inexpensive devices promise a further popularization of this powerful technique even in out-of-lab applications.[9] [10]
1.2.7.
Principles of NMR
[11]Non-zero spin nuclei which precess around their own axis (precession of the angular momentum vector) create weak magnetic dipoles which remain randomly oriented so that the net magnetization is 0. In the external magnetic field B0 (Fig. 2) those dipoles are forced to align along the magnetic field. For nucleus with a nuclear spin of ½ (like proton) there are only two magnetic states of this alignment available, lower energy parallel and higher energy anti-parallel. The difference between these two states (ΔE= γћB0 or otherwise (γh/2π)B0) which leads to the net magnetization vector parallel to the external magnetic field (M0 on Fig. 2A), is proportional to the strength of the magnetic field and the nature of the nucleus (γ – gyromagnetic ratio) but it generally remains small (10-25 J for a proton in the field of up to 15 T) what corresponds to the radiofrequency wavelengths (RF). In the consequence only a small excess of the nuclei in the lower energy level exists, being responsible for a low sensitivity of the NMR as only a tiny fraction of the whole spin population (at common fields approximately 5 in 1 000 000 [12]) will contribute to the signal (magnetization vector M0 in Fig. 2A) in the resonance experiment.
Chemical shift-based detection. The RF energy absorbed by the resonating nucleus, often described as a Larmor frequency ν0 = (γ/2π)B0 (Fig. 2B) depends in fact on the effective magnetic field experienced locally (net result of the B0 and local magnetic fields). Thus, populations of nuclei in different electronic environment (bonding geometry and character, scalar and spatial coupling, unpaired electrons, etc) will absorb at slightly different frequencies which can be transformed into field-independent characteristic values of chemical shifts. Paramagnetic quality within the sample will significantly modify the local magnetic field and thus may be detected by the observation of the change of chemical shifts, like in the Evans method for determination of the magnetic moment (see experimental part).[13] This characteristic may be potentially used for detection purposes by the Magnetic Resonance Spectroscopy or in paraCEST contrast agents for MRI.
Relaxation-based detection. Upon the absorption of the energy, the direction of the spin precession (longitudinal component of the M0 magnetization vector) and its phasing (transversal component) change (Fig. 2B). The degree of this alteration is dependent on the duration of the excitation impulse (B1) as well as its direction (90 o or 180 o). When the RF is stopped, then the system returns to the original ground state (relaxes) (Fig. 2 C). Revival of the longitudinal component characterized by the relaxation time T1 results from the nuclear spins coming back to the ground state (parallel orientation) by emitting the energy to the environment, and thus it is sometimes described as a spin-lattice relaxation. The T2 transversal relaxation time describes the dephasing process which is much faster than the longitudinal relaxation (T2 is shorter than T1) and occurs upon the spin-spin interactions. When the influence of the local inhomogeneities in the
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Fig. 2 Schematic behavior of spins in NMR experiment. A) when the sample is placed in the external field, alignment of the spins lead to net magnetization vector M0 (all spins in phase – no transversal contribution). B)
Resonance radiofrequency impulse is applied leading to the loss of longitudinal contribution and gain (phasing) of the transversal one C) recovery of longitudinal vector (T1 relaxation time) and loss (dephasing of spins) of
transversal one (T2). Taken from Doan et al 2013 [11] – reproduced by permission of WILEY-VCH Verlag
GmbH & Co. KGaA, Weinheim (copyright © 2013).
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1.3.
Magnetic Resonance Imaging in the detection of
paramagnetism
1.3.1.
General characterization of MRI as an imaging technique
One of the greatest developments in the use of NMR technique for the detection of the paramagnetic quality within the sample is Magnetic Resonance Imaging (MRI).Its importance has been acknowledged with the Noble Prize in Physiology or Medicine to Paul C. Lauterbur and Sir Peter Mansfield in 2003 for their discoveries in the field. MRI is particularly appreciated for its superb spatial resolution of soft tissues (50 µm or even down to 10 µm x 10 µm x 10 µm voxel – the size of the cell – with over 9 T experimental magnets [15]) and virtually no penetration limits.[16] As it relies on the magnetic field and radiofrequency wavelengths in order to create an image, it has all the characteristics of the magnetic signal previously described (chapter 1.3.1). In particular, it does not use any harmful, highly ionizing radiation, unlike other competing imaging tools such as Positron Emission Tomography (PET), Computed Tomography (CT), Single Photon Emission Computed Tomography (SPECT) or X-Ray.[16] and thus it might be used on everyday basis in the clinics (the number of MRI examinations for the patient is not as strictly limited as with other methods mentioned). In consequence, regardless of rather low sensitivity (10-9 to 10-6 mole of the agent detectable) [16] MRI is currently one of the main medical imaging modalities widely used in everyday clinical practice. Yet, despite intensive research in the past decade, it furnishes almost exclusively anatomic information, still awaiting a truly functional molecular probe. This development promises a creation of the incomparable tool to precisely study not only a biomedical targets, but thanks to the MRI tunability to virtually any media, also other even the most sophisticated and spatially structured samples.[1][16]
One of the prominent advantages of the MRI, especially when compared to the other techniques for paramagnetism detection, is a multidimensional imaging of even highly complex samples. The information on the precise localization of the signal is encoded by the differences in its frequency and phase from each separate voxel, obtained thanks to the application of the linear field gradient in three distinct directions. On the other hand, contrast in the image is a direct consequence of the spatial difference in the signal intensity of selected nucleus, usually water protons (it is an obvious choice for biomedical applications due to their abundance in the body). It may stem from the difference in the concentration (spin density) as well as from the variation of a T1 and/or T2 relaxation times. The image “weighting” which implies the selective measurement of the contribution of only one of these parameters, is possible by a careful choice of the signal acquisition protocol. Spin density-weighted contrast is often too small for diagnostic purposes as many soft tissues have similar water. On the other hand relaxation time-weighting allows for much more pronounced heterogeneity of the signal intensity and thus is preferred in the clinical practice. Despite the fact that the intrinsic differences in the T1 and/or T2 of the sample compartments may
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sometimes be sufficient, contrast agents (CAs) are commonly used to increase this gap and improve the sensitivity and quality of the image.[17][13][11]
1.3.2.
Role of contrast agents
MRI CAs catalyze the relaxation process of the neighboring water protons significantly improving the sensitivity of the detection and enabling the distinction between the soft tissues of close intrinsic relaxation properties. In practice, at the end of the last decade around 35 % [17] to even 40-50 % [13] of all the MRI exams were performed with a use of CAs. They can target either T
1, T2 or both at the same time. Two types of the relaxation catalysts are generally used. Superparamagnetic iron oxide nanoparticles (SPIO or ultrasmall SPIO – USPIO) principally reduce the transversal relaxation time T2, what means the loss of the transversal component and thus is associated with darker regions in the T2-weigthed Magnetic Resonance (MR) image. The diagnostic potential of this ‘negative contrast’ is limited due to the other possible reasons leading to the loss of signal in MRI than the presence of the CA, and as their chemical nature is also not relevant to the subject of this work, they will not be further discussed. Second, and by far more commonly used CAs, which are involved in 90 % of all CAs-assisted MRI examinations in clinics belong to the family of paramagnetic metal complexes and target T1, even though their effect on T2 can also be observed. Reduction of the T1 is however more attractive because it is significantly longer that T2, thus its shortening can be more pronounced and allows for increasing the number of scans in the same time period, leading to the increase in signal intensity (lighter regions on the image). The positive contrast induced by them can then be more unambiguously associated with the contrast agent activity.
From now on I will focus entirely on the T1-relaxation, even though some of the considerations below could be valid also for T2.In the following chapter I will first discuss the mechanism of longitudinal relaxation and its dependency on the intrinsic parameters of the contrast agent. Then the designs of responsive (“smart”) agents and their suitability for imaging molecular targets will be summarized.
1.3.3.
Effectiveness of T
1-CAs - Paramagnetic Relaxation Enhancement theory
As mentioned above, longitudinal relaxation (described by T1) happens upon the spin-lattice interactions, the lattice (movement of the spins) being an origin of local fluctuations in the magnetic field. Increasing the field inhomogeneities or the efficiency of their interaction with water protons (or other relaxed nuclei) will shorten the T1. In diamagnetic solutions, the relaxation occurs thanks to the magnetic field generated by the neighboring protons and thus is promoted by the increased proton density (concentration of the solvent).
Introduction of the unpaired electrons (paramagnetic quality), which have much higher magnetic moment than protons (µe = 658 µp), may catalyze the relaxation much more efficiently. This
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fundamental effect lies behind the concept of the use of paramagnetic metal ions as T1 but also T2 -CAs in MRI. [18]
Theory which describes the efficiency of the relaxation of solvent nuclei in the presence of the paramagnetic compounds is often abbreviated PRE (paramagnetic relaxation enhancement). In general the observed relaxation rate 1/T1,obs is a sum of the intrinsic relaxation rate (background relaxation rate, sometimes reduced to a diamagnetic contribution 1/T1,d) and the relaxation rate stemming from the presence of the paramagnetic substance:
(2)
Paramagnetic relaxation rate is directly proportional to the concentration of the paramagnetic compound [CA] (in mmol/l or mmol/kg of the solvent in higher density samples) by the contrast-agent specific factor of relaxivity r1 ([mM-1s-1]), which is a function of its paramagnetism and its interaction with a water protons.
(3)
Relaxivity can then be decomposed into the inner (r1IS) and outer sphere (r1OS) contributions, with a second sphere contribution r1SS being sometimes separated from the latter.
r
1= r
1IS+ (r
1SS+ r
1OS)
(4)Outer sphere contribution. The r1SS is generally small (around 10 % of the total relaxivity of classic GdIII complexes) [18] and increases only when there exist sites on the periphery of the complex allowing for specific binding of water molecules (and is a sum of relaxation rates of each of these sites). On the other hand, r1OS which refers to PRE of freely diffusing bulk solvent molecules in the proximity of the complex is not fully understood and thus difficult to be controlled. These contributions can be estimated experimentally on the basis of relaxivity of structurally similar complexes but with closed coordination sphere. Thus, r1OS was found to amount to the value of at least 1.8 - 2.5 mM-1s-1 for Gd(III) with S = 7/2 and T1e in a range of 0.1 - 1 ns (half of the r1 = 4.1 mM-l s-l of Gd-DOTA at 37 oC and 20 MHz), with values for other metals being 1.1-1.3 mM-l s-l for Mn(II) (S = 5/2, T1e of 10 – 100 ps), 0.73 - 0.95 mM-1 s for Fe(III) (S = 5/2 and T1e 1 – 100 ps) [19] and only 0.05 - 0.1 mM-1s-1 for Dy(III) (T1e = 0.1 – 1 ps).[20] These data suggest a major role of longer electronic relaxation times in increasing the outer sphere contribution, with the magnetic moment being of secondary importance (for more details see [20] and [21]).
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Inner sphere contribution to the overall relaxation rate of the protons of the bulk solvent stems from the enhanced relaxation rate of the protons of directly coordinated water molecules (denoted as 1/T1m), which exchange with the bulk solvent at average rate of 1/τm (τm - residence time), and can be described by the following equation:
(5)
where Pm is a molar fraction of bound water, equals to number of water molecules in the first coordination sphere (q) multiplied by concentration of the contrast agent [CA] and divided by water concentration, which in diluted solutions is 55.55 M.
In the light of this equation and the discussion above the number of first coordination sphere water molecules will have a direct effect on increasing the relaxation rate of the bulk (direct proportionality). Primary significance of shortening the water residence time τm is the increased number of molecules of bulk solvent which can experience the PRE. However, if paramagnetically-driven relaxation is longer than the time the water molecule spends coordinated to the metal ion, then shortening of τm has much lower significance and the process is principally T1m-determined. That is true for most practical examples of gadolinium-based contrast agents (GBCAs), where the T1m is in the range of microseconds, with τm being one to few orders of magnitude shorter, and so the understanding of the T1m regulation is of primary importance for interpreting and improving their relaxivity. Nevertheless for other systems of slower average water exchange rate, including for example Fe(III) but even Fe(II), the τm control might be dominant.
1.3.4.
Relaxation of inner sphere water - Solomon-Bloembergen-Morgan theory
Determination of the relaxation rate of bound water protons (1/T1m) is possible from a set of analytical equations (see below) constituting Solomon-Bloembergen-Morgan theory (SBM), summarized by Kowalewski et al.[22] Despite important limitations of this model (see paragraph at the end of this chapter and [22][21]) developed principally for Gd(III)-based small complexes, it will be shortly addressed below due to its utility in the interpretation of many experimental results as well as in rational design of new contrast agents with desired properties.Relaxation of water protons bound to a paramagnetic center happens principally via the dipole-dipole interactions (DD) and scalar coupling (SC) (in high field contribution of Curie spin relaxation (CS) might appear [23]) which lead to separate but additive contributions 1/T1DD + 1/T1SC. The relevant equations (taken from Toth et al 2013 [18]) are presented below but only the DD term will be discussed as the SC (might be important for Mn(II) complexes) is negligible for Gd(III) due to the highly ionic character of its bonds and significant distance between the water proton and the metal center, lowering the hyperfine coupling.
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(6)
where γI stands for the nuclear gyromagnetic ratio, g denotes the electron g-factor, rGdH is a distance between the proton and the electron spin (here of Gd ion but generally also any other electron spin), ωS and ωI are the Larmor frequencies of electron and proton respectively and τc is the correlation time characteristic of the relaxation process, described by the following equation:
(7)
where τR, Te and τm are rotational, electronic and inner sphere water residence correlation times respectively. Scalar contribution is, in turn, depicted as:
ℏ
(8)
Where A/
ℏ is a hyperfine (or scalar) coupling constant between the proton of water in the
first coordination sphere and the electron spin of the paramagnetic center and τ
eis the
appropriate correlation time, characterized as: ε
(9)
Number of unpaired electrons, which is a crucial determinant of the paramagnetism (magnetic moment) of metal complexes, is also a primary parameter influencing the relaxation rate. According to the SBM theory, relaxation rate 1/T1m is proportional to S(S+1) where S is the electronic spin of the metal ion. Indeed, 7 unpaired electrons of gadolinium(III) are principally responsible for the unbeatable relaxivities of Gd(III) based complexes. Nevertheless, transition metals like Fe(
III
) and Mn(II
) (5 unpaired electrons) or even Fe(II) (4 unpaired electrons in the high spin state - HS) could also be potentially considered. For the latter however, the relationship between the number of unpaired electrons and the relaxation rate is more complex, but the general rule that higher number of unpaired electrons mean higher relaxivity, still applies (with rough approximation – for more information please refer to limitations of the SBM theory below and also for example [22][18]).Distance r(M-H) between the unpaired electrons and water protons (often approx. to the distance between the point charges at the nuclei) has significant influence on relaxivity as the dipole-dipole interactions (major contribution to the relaxivity) are highly distance sensitive (factor of 1/r6). This parameter can be usually only slightly modified by tilting the plane of coordinated water molecule
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(difficult to control) or increasing delocalization of electrons on the ligand (higher covalency of the interaction, explorable for anisotropically distributed d-electrons of transition metals). For most Gd(III) complexes r(M-H) is around 3.1 Å and by SBM theory shortening it by 0.1 Å increases r1IS by 20 %, lengthening by 0.2 Å, in turn reduces r1IS by 50 %.[18].[20]
Correlation time τc (and τe)should be maximized and not exceed the reciprocal of a Larmor frequency (the 2τ
c2 is then either negligibly small or equal to 1). Water residence time can also influence the relaxivity by influencing this parameter, but its contribution is significant only when τm is shorter than both Te and τR (for Gd(III) it may happen at low to medium fields of 0.05 to 3 T what corresponds to 2 to 125 MHz) - for macromolecular complexes in which rotational correlation time is prolonged Fig. 3).
Long electronic relaxation time Te is the second crucial parameter of Gd(III) ion (10-6 s) which ensures its high relaxation potential in comparison to other metals, including lanthanides. Complex dependency of Te on the external magnetic field, symmetry of the complex, rotational motion and degeneration of the valence orbitals, among others, will not be discussed. It suffices to say that according to the SBM, it decreases with the square of the field,[20][24] what globally reduces r1IS, provided its crucial contribution to τc (equation 7 of SBM) which for classic small-molecule Gd(III) complexes is negligible.[18] However for other metals it might be a crucial and limiting parameter (Fe(III) or Fe(II) for example, which may have Te of as low as 1 ps).[20]
Rotational correlation time τR is probably the most extensively used feature to modify the
relaxivities of CAs as it promises the highest gains, incomparable with those attainable by realistic changes of any other parameters.[20] Slowing down the molecular movement is principally achieved by binding to the macromolecule or construction of oligomeric species. Restricted rotation by a creation of the confined cavity is also an option. However, with the increasing magnetic field, this effect is lost (for Gd(III) above 100 MHz – Fig. 3) and thus in the future applications with a much more powerful magnets allowing for higher resolution and increased sensitivity, is of no importance for Gd(III).
Fig. 3 Field dependency of relaxivity as a function of rotational correlation time, given for two different water residence times – lines are predictions on the basis of SBM theory. Reproduced from Hermann et al 2008 [17] - by
permission of The Royal Society of Chemistry (RSC) for the Centre National de la Recherche Scientifique (CNRS) and the RSC (doi: 10.1039/B719704G).
